32.10.13 problem Exercise 35.13, page 504

Internal problem ID [6007]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
Problem number : Exercise 35.13, page 504
Date solved : Sunday, March 30, 2025 at 10:31:03 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y y^{\prime \prime }-3 {y^{\prime }}^{2}&=0 \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 33

ode:=y(x)*diff(diff(y(x),x),x)-3*diff(y(x),x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= \frac {1}{\sqrt {-2 c_1 x -2 c_2}} \\ y &= -\frac {1}{\sqrt {-2 c_1 x -2 c_2}} \\ \end{align*}

✓ Mathematica. Time used: 0.11 (sec). Leaf size: 14

ode=y[x]*D[y[x],{x,2}]-(D[y[x],x])^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 e^{c_1 x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*Derivative(y(x), (x, 2)) - 3*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(3)*sqrt(y(x)*Derivative(y(x), (x, 2)))/3 + Derivative(y(x), x) cannot be solved by the factorable group method